Let vd(ℙ2) ϵ |Oℙ2(d)| denote the d-uple Veronese surface. After studying some general aspects of the wall-crossing phenomena for stability conditions on surfaces, we are able to describe a sequence of flips of the secant varieties of vd(ℙ2) by embedding the blow-up blvd(ℙ2) |Oℙ2(d)| into a suitable moduli space of Bridgeland semistable objects on ℙ2.